© Harold Aspden, 1998

Research Note: 7/98: September 28, 1998

I am writing this in response to a challenge. The nature of the challenge, which concerns supergraviton theory, chaos theory and a conflict between the mathematical and the physical approach to the interpretation of what we observe in nature is not of any special interest; it is a matter which concerns myself and my challenger. The crucial point involved concerns the precise value of the heavy lepton known as the 'tau' or taon'. However, I seek here to record my comments on how mother Nature determines that mass, because I have at this time confronted this issue and just wish to put my findings on record. They are of general interest only for those who have understood some of the more advanced features of my theoretical investigations concerning the fundamentals of gravitation

When I embarked on the task of building a viable theory of gravitation, linking G, the constant of gravitation with electromagnetic field theory, I was unaware of the role that the tau particle might play in the dynamics of the balancing act as between matter and the ghostly underworld of the background aether. Indeed, since that was back in the 1950s, I had no reason to suspect such a connection, given that the tau lepton had not been discovered. Cosmic ray mesons had come onto the physical scene in the 1935 period, thanks to Yukawa theorizing about exchange forces between nucleons and mesons made their experimental debut at about the same time in the work of Anderson and Nedermeyer, but it took until 1947 before the picture clarified as between two meson forms, the pi-meson or pion and the mu-meson of muon.

The latter belongs to the lepton family. It is a heavy electron, but it was to be many years on before the even heavier lepton, the tau or taon was discovered.

So far as the early development of my theory of gravitation is concerned, this was wholly concentrated on the role played by the aether in separating chaos from order in the ongoing interplay between aether and matter, and to me matter was something composed of proton-sized particles plus that abundant lepton form we call the electron.

However, I will here contrast the state of my theory in the late 1950s period with its developed form I now see as its 21st century status.

Fig. 1
Referring to Fig. 1, my picture of our presence in an aethereal environment is one in which matter comprising electrons and protons exist in what I call the E-frame. The whole of this frame moves with a circular gyratory motion at the Compton electron frequency, the frequency we associate with the wave properties of the electron. This puts the E-frame out-of-balance dynamically unless there is something acting as a counter-balance. This I call the G-frame. There had to be something hidden in this G-frame to set up that balance. It had to exhibit mass and yet not reveal itself in our experiments, except, that is, for the role it plays in determining G and setting up the force action we call gravity.

Now back in the 1950s, I contrived to devise a quantum theory of gravity, imagining that perhaps the neutrino was at work in conjunction with a proton-sized unit of mass, the neutrino being deployed in the G-frame, where its motion in its dynamic association with the proton-sized unit of mass 'carved-out', as it were, a hole in the electrical background continuum of the aether. The motion of that hole was seen as setting up the electrodynamic action which gave the force of gravity.

If you wish to inspect the version of my theory as it stood at year-end 1959 then refer to: The Theory of Gravitation.

The key feature of that theory is the explanation of how the aether sets up the framework for regulating Planck's quantum of action. That gives a definitive evaluation of the fine-structure constant, the fundamental constant of quantum theory, and it determines the parameters from which we can deduce G, the constant of gravitation, in terms of the charge/mass ratrio of the electron.

The analysis points to the existence of a cubic array of aether particles, otherwise called lattice particles, or, as now in Fig. 1, 'quons', and these form an ordered background system prevailing throughout all space. Everything else is in at least a partial state of chaos, and, so far a concerns the E-frame, we and the matter form we represent constitute something that amounts to a modest amount of chaos sharing the underlying rhythmic motion of that E-frame.

Take note here that the Heisenberg Principle of Uncertainty implies an underlying order in the motion of all material particles. Their momenta might be uncertain and their position uncertain, as they describe those orbits in their rhythmic jitter motion at the Compton electron frequency, but, for electrons, the product of momentum and displacement from the inertial frame (the I-frame) is certain, it being h/2.

So, back in the 1950 period my theory pictured what is shown in Fig. 1, but it lacked the presence of those muons in the I-frame.

Physicists have long admitted that they have no idea as to how muons feature in the scheme of things. They are not seen as building blocks in the particles of matter, but they are known to decay into electrons and can appear as decay products in particle transmutations.

Now, as my theory developed, I came to realise that those gravitons in Fig. 1 existed in three forms, namely the g-particle or basic graviton, which has a mass somewhat less than that of three protons, the tau, which has a mass nearly twice that of two protons and the supergraviton, which has a mass of about 100 times that of the proton. The prevalent form is the combination of the g-particle and the tau in the presence ratio of one to two, meaning that there are generally two tau particles for every g-particle. The supergravitons come into being when the mass density of matter in the E-frame is high so that the lepton activity of pair creation and annihilation adapts in an optimum fashion to provide that dynamic mass balance. This is necessary when atoms in the upper half of the periodic table are present.

In Fig. 1 you can see that I have included the word 'virtual' in the G-frame section. This indicates that the particles here are the transiently stable charge forms that one can associate with pair creation and annihilation in quantum electrodynamics. In this sense electrons in their free state are also virtual, but I am using this expression 'virtual' to distinguish between states which are bare electric charge forms and those which are part of composite structures, the latter assuring a quasi-stability and so being their form as seen sporadically in matter generally.

The muon, for example, has, according to my theory a theoretical form in which it would, if part of the G-frame, exhibit a mass that is not the same as that of the muon as seen and measured in our experiments. There is a slight difference owing to the fact that the 'real' muon is really a 'virtual' muon nested between two electrons or two positrons, according to its polarity.

To appreciate what I am saying about that it is necessary to refer to my published scientific papers on that subject, namely the two papers 'The Nature of the Muon' and 'The Mass of the Muon' published in 1983 in Lettere al Nuovo Cimento, an English language scientific periodical published at that time by the Italian Institute of Physics, [1983e] and [1983h].

A further feature or 'discovery' which crept into my theory as it developed, and has been mentioned in my writings (see the reference to C A Bjerknes at page 52 in my 1996 book Aether Science Papers), is that charge polarity has its physical embodiment as a state of phase in the radial oscillation of the unitary charge form of a fundamental particle. In other words, charges we say are 'positive' are really, so far as Nature is concerned, alternating between 'positive' and 'negative' in anti-phase with the oscillations of 'negative' charges. Essential to this is that synchrony of action that governs the aether system as a whole in its electrostatic behaviour.

One cannot, however, rule out the possibility that the oscillations can be very much more rapid in particle forms that confine their energy into a smaller space. Thus the tau particle, meaning the one we 'see' in our experiments, might well be changing polarity state internally, but yet overall keep an apparent steady polarity as referenced on the polarity of the electron.

Fig. 2

To understand this refer to Fig. 2. This shows the electrons of negative polarity, but the tau and the muon can have either polarity. Indeed, they can flip between polarity states as the composite tau-particle form flips between State A and State B. The process involves the background aether in an energy fluctuation such as is involved in creating an electron-positron pair in quantum electrodynamics, but since charge polarity has to be conserved the action creates instead the two electrons shown in the State B composition.

This process is somewhat analogous with that discussed in my paper 1986d concerning the neutron and the deuteron.

Though this may seem to be hypothesis, I would rather say that it is the interpretation of evolving facts, facts provided by the precision measurement of the particle involved, namely the tau.

When I first introduced the tau into my theory and discovered its role as a graviton the tau had a reported mass value several MeV greater than that I calculated as being the true mass of the virtual-tau in its gravitational role. As the years moved on I found that the measured value sank below the one I had calculated. That allowed me to verify an analogy related to the similar scenario I had encountered in theorizing about the muon and I was greatly heartened by the result. You may judge this for yourself by reference to a section incorporating page 12 of my 1996 work Aether Science Papers.

The analysis in that latter work was based on the picture of the tau as being that shown in State A of Fig. 2 above.

I quote from that work:
"Now I have, above, mentioned the 'harmonics of the primes', having in mind the wave resonances and standing wave effects that can control the deployment of energy in particle groups. Such effects have been recognized in my researches in connection with the proton and neutral pion, as mentioned below. Also, in 1972, I had adopted the odd integer space volume quantization to derive the fine-structure constant [Physics Letters, 41A, 423 (1972)]. Later, the evidence pointed to the wave resonance as well, so that in 1983 I did explain why the 'aether' muon or 'virtual' muon, being a bare muon, had a mass slightly below that of the real muon, the one having a electron retinue. Referenced on the integer mass ratio 207, the applicable formula, to a first approximation is:
mμ/m = 207 + 2 - (9/4)(207)/(207+3)
which is 206.7687. The second Lett. Nuovo Cimento paper referenced above gave reason for 'tuning' this to a slightly lower value, bringing it into perfect accord with the measured value of 206.7683.

What I now declare as being extra proof and vindication of my research in arguing in support of the wave resonances just mentioned, is the fact that the real taon should replicate the muon situation by having a retinue of two virtual muons, whereas the muon had a retinue of two virtual leptons of electron size. The number 207 can be replaced by 17, at least to a first approximation, because the taon is that much more massive than the muon. Accordingly 17 can replace 207 in the above equation to give:
mτ/mμ = 17 + 2 - (9/4)(17)/(17+3)
which is 4.43 Mev below the value of mτ corresponding to the factor 17, if mμ/m is 207. So the 1780.94 MeV estimate of the virtual taon mass indicates a 'real' taon mass of 1776.51 MeV, whereas the value, as now reported, is 1777.1 +/- 0.5 Mev."

Now, as time has moved on, the mass of the tau particle has been measured to even greater precision as being 1777.05 MeV with an uncertainty of 0.02 MeV. Looking at Fig. 2 one can see that, on average, the mass of the tau-particle will be one electron mass unit (0.511 MeV) above that of State A, assuming that the tau-particle spends half its time in State A and half in State B, which is logical for the oscillatory action. Thus the theoretical value of the tau mass is increased from 1776.51 MeV to 1777.02 MeV and that again shows that my theory can hold its ground.

Should you wonder why all this is important, my answer is that I have a theory of gravitation which is part of a unified account embracing the various particle forms which physicists study and measure with precision. Why do they make such measurements? Surely it is to provide data helpful in evolving theories and so strengthening our knowledge of Nature. Why else would they measure the mass energy of a particle that they regard as quite exotic and ostensibly serving no special role. My theory recognizes that the tau has a role in a unified theory connecting gravitation and electromagnetism. The precision measurement of the tau mass is therefore something that adds more confirmation in support of my theory.

So far as the 'challenge' is concerned, the one I mentioning in introducing this Research Note, I just note that my challenger was seeking to disprove my theoretical association of the tau particle with the graviton form and, in particular, with the supergraviton form, which he deemed had a value determined by number theory as applied to 'chaos'. The route he suggested left no structure by which to connect physically with the force of gravitation, and far less to derive a theoretical value for G, the constant of gravitation. Hence I am obliged to confine my response to the 'challenge' to this showing that the updated measurement of the tau mass is still within the scope of my theory.

Harold Aspden
September 28, 1998